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Beyond the intradimer [2 + 2] cycloaddition chemistry of ethylene on Si(1 0 0): theoretical evidence on the occurrence of interdimer reaction
Chemical Physics Letters 393 (2004) 124–127 www.elsevier.com/locate/cplett
Beyond the intradimer [2 + 2] cycloaddition chemistry of ethylene on Si(1 0 0): theoretical evidence on the occurrence of interdimer reaction Xin Lu *, Mengping Zhu Department of Chemistry, State Key Laboratory of Physical Chemistry of Solid Surfaces and Center for Theoretical Chemistry, Xiamen University, Xiamen 361005, PR China Received 2 May 2004
Abstract Density functional cluster model calculations reveal that in addition to the well-accepted intradimer [2 + 2] cycloaddition, interdimer [2 + 2] cycloaddition as well as the parallel end-bridge mode adsorption should play an important role in the technologically important alkene/Si(1 0 0) chemistry. Ó 2004 Elsevier B.V. All rights reserved.
1. Introduction Intensive interest has been focused on the organic functionalization of semiconductor silicon surfaces in recent years. Abundant and intriguing organic/silicon surface chemistry has been disclosed [1–4]. Of great technological importance is the finding that adsorption of simple alkenes such as ethylene on Si(1 0 0) can lead to the formation of controllable and uniform organic monolayer on the semiconductor surface with strong organic–silicon binding [1–8]. The chemistry underlying is now well accepted, i.e., a simple alkene is adsorbed on a Si@Si dimer of the reconstructed Si(1 0 0)-2 1 surface, in effect analogous to the [2 + 2] cycloaddition of two alkenic molecules in organic chemistry [1–12]. However, the [2 + 2] cycloaddition in organic chemistry is symmetry-forbidden and thermally inaccessible. Controversy thus arose on the mechanism of the thermally facile, but seemingly ‘symmetry-forbidden’, heterogeneous [2 + 2] cycloaddition of alkene on Si(1 0 0) [10–12]. By means of density functional cluster model calculations, we have recently demonstrated that adsorption *
Corresponding author. Fax: +86-592-2183047. E-mail address: [email protected] (X. Lu).
0009-2614/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2004.06.023
of ethylene on a Si@Si dimer of Si(1 0 0) surface follows a diradical pathway via a p-complex precursor 1 and a singlet–diradical intermediate 2, leading finally to formation of the intradimer [2 + 2] cycloaddition product 3 (path I in Scheme 1) [12]. Such a diradical mechanism was supported by the STM observation[11] that the adsorption of an alkene on Si(1 0 0) is not stereospecific, but highly stereoselective, in nature. It is the weak pbond of the surface dimer that facilitates this diradical pathway. Furthermore, the presence of the singlet–diradical intermediate 2 in the intradimer [2 + 2] adsorp-
Scheme 1. Proposed pathways for the adsorption of a simple alkene on the Si@Si dimers of Si(1 0 0) surface.
X. Lu, M. Zhu / Chemical Physics Letters 393 (2004) 124–127
tion inspires us with the possibility that interdimer [2 + 2] adsorption 4 may occur if the radical end of 2 attacks a neighboring Si@Si dimer (path II in Scheme 1). Such an interdimer process would produce two radicallike dangling bonds at the unreacted ends of two neighboring surface dimers, which should be subject to
125
adsorption of a second ethylene molecule to form the parallel end-bridge (PEB) adsorption mode 5. Herein we report theoretical evidence that in addition to the wellaccepted intradimer [2 + 2] adsorption, interdimer [2 + 2] adsorption of an alkene on Si(1 0 0) surface is also accessible via the diradical intermediate 2 and thus could
Fig. 1. (U)B3LYP/6-31G* optimized intermediate (LM1), transition states (TS1, TS2 and TS3) and products (LM2, and LM3) for the intradimer and interdimer [2 + 2] cycloadditions of ethylene on Si15 H16 cluster model. Energies (DE in kcal/mol) relative to isolated ethylene and Si15 H16 as well as hS 2 i values for the wave functions of these stationary points are also given.
126
X. Lu, M. Zhu / Chemical Physics Letters 393 (2004) 124–127
not be excluded from the technologically important alkene/Si(1 0 0) chemistry.
2. Computational method and model Our density functional cluster model calculations were performed at the (U)B3LYP/6-31G* level of theory[13,14] with GA U S S I A N 98 [15]. A Si15 H16 cluster model was used to represent two neighboring Si@Si dimers of Si(1 0 0) surface [16–21]. Geometrical optimizations were performed with constraints at the third- and fourth-layer substrate atoms and at the Hsaturators [19,20]. Details of the geometric constraints can be found in the previous theoretical investigations on the reactions of H2 O and NH3 with Si(1 0 0) reported by Queeney et al. [19,20]. Reported energies have not been corrected with zero point energy (ZPE), unless otherwise specified. The predicted intermediates, transition states and products are depicted in Figs. 1 and 2.
3. Results and discussions In our previous study of the intradimer [2 + 2] cycloaddition [12], we used a single–dimer Si9 H12 cluster to model a Si@Si dimer of Si(1 0 0) surface and found that formation of the singlet–diradical intermediate 2 is the rate-determining step with an overall activation energy of 4.2 kcal/mol (ZPE-corrected value) [12]. In the present study, we find that on the double-dimer Si15 H16 cluster model the transition state TS1 (Fig. 1a) responsible for formation of the singlet–diradical intermediate 2 (LM1 in Fig. 1b) is by 5.2 kcal/mol higher than isolated reactants. Upon ZPE-correction the activation barrier at this transition state is reduced to 1.5 kcal/mol, by 2.7 kcal/mol lower than the previous prediction. Thus larger cluster model tends to lower the predicted activation energy for the adsorption of ethylene.
Fig. 2. B3LYP/6-31G* optimized geometry of the parallel end-bridge mode for the adsorption of two ethylene molecules on the double-dimer cluster model. Energy (DE in kcal/mol) relative to isolated ethylenes and Si15 H16 .
Fig. 1b depicts the singlet–diradical intermediate (LM1) formed on the double-dimer cluster model. From LM1, the intradimer [2 + 2] product (LM2) can be readily formed by overcoming a very small barrier (0.4 kcal/mol) at the transition state TS2. Such an intradimer [2 + 2] process is predicted to be exothermic by 43.5 kcal/ mol relative to isolated reactants. Note that an exothermicity of 44.9 kcal/mol was predicted in our previous work using the single–dimer cluster model [12]. Thus cluster size effect is trivial on the predicted exothermicity of the intradimer [2 + 2] adsorption. In short, both the double-dimer and single–dimer cluster models are capable of predicting the diradical pathway for the intradimer [2 + 2] process. As shown in Fig. 1, from the singlet–diradical intermediate LM1, interdimer [2 + 2] adsorption can also occur through a transition state TS3, leading to formation of the interdimer [2 + 2] product LM3. Such an interdimer process with a predicted exothermicity of 32.1 kcal/mol appears to be less exothermic than the intradimer [2 + 2] cycloadition, probably due to larger steric strain within the interdimer [2 + 2] product. Note in the interthat the interdimer distance is only 3.54 A dimer [2 + 2] product, compared to 3.97 A in the intradimer product and in the unreacted double-dimer model. TS3 is located by only 0.5 kcal/mol higher than LM1 in energy. Noteworthily, the large hS 2 i value (1.46) of TS2 suggests this transition state is not purely singlet– diradicaloid, but partially singlet–tetraradicaloid in nature. The interdimer [2 + 2] product LM3 is singlet–diradicaloid in nature, as indicated by its nearly unity hS 2 i value. The reaction of LM3 with a second ethylene is predicted to be highly exothermic by 44.3 kcal/mol, giving rise to the parallel end-bridge (PEB) adsorption mode (Fig. 2). The overall formation energy of PEB is 76.4 kcal/mol from isolated ethylenes and cluster model. At present, direct experimental evidence on the occurrence of interdimer [2 + 2] cycloaddition of an alkene on Si(1 0 0) is not available yet. It should be mentioned that two ethylene TPD peaks at 620 and 650 K were revealed in the TPD experiments on the ethylene/ Si(1 0 0) chemisorption system and were attributed to desorptions from the intradimer [2 + 2] adsorption mode and from defect sites, respectively [6,7]. Very recently, Kim et al. [21] found similar two-state desorption behavior on the analogous ethylene/Ge(1 0 0) system, but their STM experiments clearly indicate the presence of the intradimer [2 + 2] adsorption mode and interdimer PEB adsorption mode. Furthermore, both intradimer and interdimer cycloadditions were revealed in the adsorption of acetylene [22–24] and 1,3-cyclohexadiene [25] on Si(1 0 0). Based on our theoretical prediction and these indirect experimental evidences, we believe that in addition to the well-accepted intradimer [2 + 2] cycloaddition, interdimer [2 + 2] process as well as PEB
X. Lu, M. Zhu / Chemical Physics Letters 393 (2004) 124–127
adsorption mode should play a nontrivial role in the technologically important alkene/Si(1 0 0) chemistry. To confirm the prediction presented here, more elaborate experiments, especially STM experiments, should be done.
Acknowledgements This work was sponsored by NSF of China (Grants No. 20021002, 20203013, 90206038 and 20023001), Fok Ying-Tung Education Foundation, Ministry of Education of PRC (Grant No. 20010384005), Ministry of Science and Technology (Grants No. G1999022408 and 2002CCA01600), and NSF of Fujian Province (Grants No. E0210001 and 2002F010).
References [1] R.A. Wolkow, Ann. Rev. Phys. Chem. 50 (1999) 413. [2] R.J. Hamers, S.K. Coulter, M.D. Ellison, J.S. Hovis, D.F. Padowitz, M.P. Schwartz, C.S. Greenlief, J.N. Russell Jr., Acc. Chem. Res. 33 (2000) 617. [3] S.F. Bent, J. Phys. Chem. B 106 (2002) 2830. [4] X. Lu, M.C. Lin, Int. Rev. Phys. Chem. 21 (2002) 137. [5] C.C. Cheng, R.M. Wallace, P.A. Taylor, W.J. Choyke, J.T. Yates Jr., J. Appl. Phys. 67 (1990) 3693.
127
[6] L. Clemen, R.M. Wallace, P.A. Taylor, M.J. Dresser, W.J. Choyke, W.H. Weinberg, J.T. Yates Jr., Surf. Sci. 268 (1992) 205. [7] A. Fink, R. Huber, W. Widdra, J. Chem. Phys. 115 (2001) 2768. [8] G.P. Lopinski, D.J. Moffatt, D.D.M. Wayner, R.A. Wolkow, J. Am. Chem. Soc. 122 (2000) 3548. [9] R.J. Hamers, J.S. Hovis, S. Lee, H. Liu, J. Shan, J. Phys. Chem. B 101 (1997) 1489. [10] H. Liu, R.J. Hamers, J. Am. Chem. Soc. 119 (1997) 7593. [11] G.P. Lopinski, D.J. Moffatt, D.D.M. Wayner, M.Z. Zgierski, R.A. Wolkow, J. Am. Chem. Soc. 121 (1999) 4532. [12] X. Lu, J. Am. Chem. Soc. 125 (2003) 6384. [13] A.D. Becke, J. Chem. Phys. 98 (1993) 5648. [14] C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785. [15] M.J. Frisch et al., GA U S S I A N 98, Gaussian Inc., Pittsburgh, PA, 1998. [16] X. Lu, X. Xu, N. Wang, Q. Zhang, M.C. Lin, J. Phys. Chem. B 105 (2001) 10 069. [17] F. Bacalzo-Gladden, X. Lu, M.C. Lin, J. Phys. Chem. B 105 (2001) 4368. [18] X. Lu, M.C. Lin, Phys. Chem. Chem. Phys. 2 (2000) 4213. [19] K.T. Queeney, M.K. Weldon, Y.J. Chabal, K. Raghavachari, J. Chem. Phys. 119 (2003) 2307. [20] K.T. Queeney, Y.J. Chabal, K. Raghavachari, Phys. Rev. Lett. 86 (2001) 1046. [21] A. Kim, D.S. Choi, J.Y. Lee, S. Kim, J. Phys. Chem. B 108 (2004) 3256. [22] S. Mezhenny, I. Lyubinetsky, W.J. Choyke, R.A. Wolkow, J.T. Yates, Chem. Phys. Lett. 344 (2001) 7. [23] P. Lal, A.V. Teplyakov, Y. Noah, M.J. Kong, G.T. Wang, S.F. Bent, J. Chem. Phys. 110 (1999) 10 545. [24] D.C. Sorescu, K.D. Jordan, J. Phys. Chem. B 104 (2000) 8259. [25] L.C. Teague, J.J. Boland, J. Phys. Chem. B 107 (2003) 3820.
Beyond the intradimer [2 + 2] cycloaddition chemistry of ethylene on Si(1 0 0): theoretical evidence on the occurrence of interdimer reaction Xin Lu *, Mengping Zhu Department of Chemistry, State Key Laboratory of Physical Chemistry of Solid Surfaces and Center for Theoretical Chemistry, Xiamen University, Xiamen 361005, PR China Received 2 May 2004
Abstract Density functional cluster model calculations reveal that in addition to the well-accepted intradimer [2 + 2] cycloaddition, interdimer [2 + 2] cycloaddition as well as the parallel end-bridge mode adsorption should play an important role in the technologically important alkene/Si(1 0 0) chemistry. Ó 2004 Elsevier B.V. All rights reserved.
1. Introduction Intensive interest has been focused on the organic functionalization of semiconductor silicon surfaces in recent years. Abundant and intriguing organic/silicon surface chemistry has been disclosed [1–4]. Of great technological importance is the finding that adsorption of simple alkenes such as ethylene on Si(1 0 0) can lead to the formation of controllable and uniform organic monolayer on the semiconductor surface with strong organic–silicon binding [1–8]. The chemistry underlying is now well accepted, i.e., a simple alkene is adsorbed on a Si@Si dimer of the reconstructed Si(1 0 0)-2 1 surface, in effect analogous to the [2 + 2] cycloaddition of two alkenic molecules in organic chemistry [1–12]. However, the [2 + 2] cycloaddition in organic chemistry is symmetry-forbidden and thermally inaccessible. Controversy thus arose on the mechanism of the thermally facile, but seemingly ‘symmetry-forbidden’, heterogeneous [2 + 2] cycloaddition of alkene on Si(1 0 0) [10–12]. By means of density functional cluster model calculations, we have recently demonstrated that adsorption *
Corresponding author. Fax: +86-592-2183047. E-mail address: [email protected] (X. Lu).
0009-2614/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2004.06.023
of ethylene on a Si@Si dimer of Si(1 0 0) surface follows a diradical pathway via a p-complex precursor 1 and a singlet–diradical intermediate 2, leading finally to formation of the intradimer [2 + 2] cycloaddition product 3 (path I in Scheme 1) [12]. Such a diradical mechanism was supported by the STM observation[11] that the adsorption of an alkene on Si(1 0 0) is not stereospecific, but highly stereoselective, in nature. It is the weak pbond of the surface dimer that facilitates this diradical pathway. Furthermore, the presence of the singlet–diradical intermediate 2 in the intradimer [2 + 2] adsorp-
Scheme 1. Proposed pathways for the adsorption of a simple alkene on the Si@Si dimers of Si(1 0 0) surface.
X. Lu, M. Zhu / Chemical Physics Letters 393 (2004) 124–127
tion inspires us with the possibility that interdimer [2 + 2] adsorption 4 may occur if the radical end of 2 attacks a neighboring Si@Si dimer (path II in Scheme 1). Such an interdimer process would produce two radicallike dangling bonds at the unreacted ends of two neighboring surface dimers, which should be subject to
125
adsorption of a second ethylene molecule to form the parallel end-bridge (PEB) adsorption mode 5. Herein we report theoretical evidence that in addition to the wellaccepted intradimer [2 + 2] adsorption, interdimer [2 + 2] adsorption of an alkene on Si(1 0 0) surface is also accessible via the diradical intermediate 2 and thus could
Fig. 1. (U)B3LYP/6-31G* optimized intermediate (LM1), transition states (TS1, TS2 and TS3) and products (LM2, and LM3) for the intradimer and interdimer [2 + 2] cycloadditions of ethylene on Si15 H16 cluster model. Energies (DE in kcal/mol) relative to isolated ethylene and Si15 H16 as well as hS 2 i values for the wave functions of these stationary points are also given.
126
X. Lu, M. Zhu / Chemical Physics Letters 393 (2004) 124–127
not be excluded from the technologically important alkene/Si(1 0 0) chemistry.
2. Computational method and model Our density functional cluster model calculations were performed at the (U)B3LYP/6-31G* level of theory[13,14] with GA U S S I A N 98 [15]. A Si15 H16 cluster model was used to represent two neighboring Si@Si dimers of Si(1 0 0) surface [16–21]. Geometrical optimizations were performed with constraints at the third- and fourth-layer substrate atoms and at the Hsaturators [19,20]. Details of the geometric constraints can be found in the previous theoretical investigations on the reactions of H2 O and NH3 with Si(1 0 0) reported by Queeney et al. [19,20]. Reported energies have not been corrected with zero point energy (ZPE), unless otherwise specified. The predicted intermediates, transition states and products are depicted in Figs. 1 and 2.
3. Results and discussions In our previous study of the intradimer [2 + 2] cycloaddition [12], we used a single–dimer Si9 H12 cluster to model a Si@Si dimer of Si(1 0 0) surface and found that formation of the singlet–diradical intermediate 2 is the rate-determining step with an overall activation energy of 4.2 kcal/mol (ZPE-corrected value) [12]. In the present study, we find that on the double-dimer Si15 H16 cluster model the transition state TS1 (Fig. 1a) responsible for formation of the singlet–diradical intermediate 2 (LM1 in Fig. 1b) is by 5.2 kcal/mol higher than isolated reactants. Upon ZPE-correction the activation barrier at this transition state is reduced to 1.5 kcal/mol, by 2.7 kcal/mol lower than the previous prediction. Thus larger cluster model tends to lower the predicted activation energy for the adsorption of ethylene.
Fig. 2. B3LYP/6-31G* optimized geometry of the parallel end-bridge mode for the adsorption of two ethylene molecules on the double-dimer cluster model. Energy (DE in kcal/mol) relative to isolated ethylenes and Si15 H16 .
Fig. 1b depicts the singlet–diradical intermediate (LM1) formed on the double-dimer cluster model. From LM1, the intradimer [2 + 2] product (LM2) can be readily formed by overcoming a very small barrier (0.4 kcal/mol) at the transition state TS2. Such an intradimer [2 + 2] process is predicted to be exothermic by 43.5 kcal/ mol relative to isolated reactants. Note that an exothermicity of 44.9 kcal/mol was predicted in our previous work using the single–dimer cluster model [12]. Thus cluster size effect is trivial on the predicted exothermicity of the intradimer [2 + 2] adsorption. In short, both the double-dimer and single–dimer cluster models are capable of predicting the diradical pathway for the intradimer [2 + 2] process. As shown in Fig. 1, from the singlet–diradical intermediate LM1, interdimer [2 + 2] adsorption can also occur through a transition state TS3, leading to formation of the interdimer [2 + 2] product LM3. Such an interdimer process with a predicted exothermicity of 32.1 kcal/mol appears to be less exothermic than the intradimer [2 + 2] cycloadition, probably due to larger steric strain within the interdimer [2 + 2] product. Note in the interthat the interdimer distance is only 3.54 A dimer [2 + 2] product, compared to 3.97 A in the intradimer product and in the unreacted double-dimer model. TS3 is located by only 0.5 kcal/mol higher than LM1 in energy. Noteworthily, the large hS 2 i value (1.46) of TS2 suggests this transition state is not purely singlet– diradicaloid, but partially singlet–tetraradicaloid in nature. The interdimer [2 + 2] product LM3 is singlet–diradicaloid in nature, as indicated by its nearly unity hS 2 i value. The reaction of LM3 with a second ethylene is predicted to be highly exothermic by 44.3 kcal/mol, giving rise to the parallel end-bridge (PEB) adsorption mode (Fig. 2). The overall formation energy of PEB is 76.4 kcal/mol from isolated ethylenes and cluster model. At present, direct experimental evidence on the occurrence of interdimer [2 + 2] cycloaddition of an alkene on Si(1 0 0) is not available yet. It should be mentioned that two ethylene TPD peaks at 620 and 650 K were revealed in the TPD experiments on the ethylene/ Si(1 0 0) chemisorption system and were attributed to desorptions from the intradimer [2 + 2] adsorption mode and from defect sites, respectively [6,7]. Very recently, Kim et al. [21] found similar two-state desorption behavior on the analogous ethylene/Ge(1 0 0) system, but their STM experiments clearly indicate the presence of the intradimer [2 + 2] adsorption mode and interdimer PEB adsorption mode. Furthermore, both intradimer and interdimer cycloadditions were revealed in the adsorption of acetylene [22–24] and 1,3-cyclohexadiene [25] on Si(1 0 0). Based on our theoretical prediction and these indirect experimental evidences, we believe that in addition to the well-accepted intradimer [2 + 2] cycloaddition, interdimer [2 + 2] process as well as PEB
X. Lu, M. Zhu / Chemical Physics Letters 393 (2004) 124–127
adsorption mode should play a nontrivial role in the technologically important alkene/Si(1 0 0) chemistry. To confirm the prediction presented here, more elaborate experiments, especially STM experiments, should be done.
Acknowledgements This work was sponsored by NSF of China (Grants No. 20021002, 20203013, 90206038 and 20023001), Fok Ying-Tung Education Foundation, Ministry of Education of PRC (Grant No. 20010384005), Ministry of Science and Technology (Grants No. G1999022408 and 2002CCA01600), and NSF of Fujian Province (Grants No. E0210001 and 2002F010).
References [1] R.A. Wolkow, Ann. Rev. Phys. Chem. 50 (1999) 413. [2] R.J. Hamers, S.K. Coulter, M.D. Ellison, J.S. Hovis, D.F. Padowitz, M.P. Schwartz, C.S. Greenlief, J.N. Russell Jr., Acc. Chem. Res. 33 (2000) 617. [3] S.F. Bent, J. Phys. Chem. B 106 (2002) 2830. [4] X. Lu, M.C. Lin, Int. Rev. Phys. Chem. 21 (2002) 137. [5] C.C. Cheng, R.M. Wallace, P.A. Taylor, W.J. Choyke, J.T. Yates Jr., J. Appl. Phys. 67 (1990) 3693.
127
[6] L. Clemen, R.M. Wallace, P.A. Taylor, M.J. Dresser, W.J. Choyke, W.H. Weinberg, J.T. Yates Jr., Surf. Sci. 268 (1992) 205. [7] A. Fink, R. Huber, W. Widdra, J. Chem. Phys. 115 (2001) 2768. [8] G.P. Lopinski, D.J. Moffatt, D.D.M. Wayner, R.A. Wolkow, J. Am. Chem. Soc. 122 (2000) 3548. [9] R.J. Hamers, J.S. Hovis, S. Lee, H. Liu, J. Shan, J. Phys. Chem. B 101 (1997) 1489. [10] H. Liu, R.J. Hamers, J. Am. Chem. Soc. 119 (1997) 7593. [11] G.P. Lopinski, D.J. Moffatt, D.D.M. Wayner, M.Z. Zgierski, R.A. Wolkow, J. Am. Chem. Soc. 121 (1999) 4532. [12] X. Lu, J. Am. Chem. Soc. 125 (2003) 6384. [13] A.D. Becke, J. Chem. Phys. 98 (1993) 5648. [14] C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785. [15] M.J. Frisch et al., GA U S S I A N 98, Gaussian Inc., Pittsburgh, PA, 1998. [16] X. Lu, X. Xu, N. Wang, Q. Zhang, M.C. Lin, J. Phys. Chem. B 105 (2001) 10 069. [17] F. Bacalzo-Gladden, X. Lu, M.C. Lin, J. Phys. Chem. B 105 (2001) 4368. [18] X. Lu, M.C. Lin, Phys. Chem. Chem. Phys. 2 (2000) 4213. [19] K.T. Queeney, M.K. Weldon, Y.J. Chabal, K. Raghavachari, J. Chem. Phys. 119 (2003) 2307. [20] K.T. Queeney, Y.J. Chabal, K. Raghavachari, Phys. Rev. Lett. 86 (2001) 1046. [21] A. Kim, D.S. Choi, J.Y. Lee, S. Kim, J. Phys. Chem. B 108 (2004) 3256. [22] S. Mezhenny, I. Lyubinetsky, W.J. Choyke, R.A. Wolkow, J.T. Yates, Chem. Phys. Lett. 344 (2001) 7. [23] P. Lal, A.V. Teplyakov, Y. Noah, M.J. Kong, G.T. Wang, S.F. Bent, J. Chem. Phys. 110 (1999) 10 545. [24] D.C. Sorescu, K.D. Jordan, J. Phys. Chem. B 104 (2000) 8259. [25] L.C. Teague, J.J. Boland, J. Phys. Chem. B 107 (2003) 3820.